Habitat selection by two competing species in a two-habitat environment

Evolution of realized niche breadth diversity driven by community dynamics

Why many herbivorous insects are host plant specialists, with non-negligible exceptions, is a conundrum of evolutionary biology, especially because the host plants are not necessarily optimal larval diets. Here, I present a novel model of host plant preference evolution of two insect species. Because habitat preference evolution is contingent upon demographic dynamics, I integrate the evolutionary framework with the modern coexistence theory. The results show that the two insect species can evolve into a habitat specialist and generalist, when they experience both negative and positive frequency-dependent community dynamics. This happens because the joint action of positive and negative frequency dependence creates multiple (up to nine) eco-evolutionary equilibria. Furthermore, initial condition dependence due to positive frequency dependence allows specialization to poor habitats. Thus, evolved habitat preferences do not necessarily correlate with the performances. The model provides explanations for counterintuitive empirical patterns and mechanistic interpretations for phenomenological models of niche breadth evolution.

Thermal threshold and interspecific competition help explain intertidal hermit crab assemblages

Habitat heterogeneity promotes species diversity by providing a variety of abiotic and biotic conditions, whose impact on performance varies among species. Then, mobile species would be expected to move to areas whose conditions maximize their fitness. However, biotic pressures such as interspecific competition can push subordinate species into suboptimal areas, impeding this matching. The tropical hermit crab Clibanarius albidigitus occupies mostly upper intertidal sites where they can experience extreme environmental conditions. Meanwhile, its stronger agonistic competitor, Calcinus californiensis, mostly inhabits more moderate conditions at the mid intertidal. We estimated the avoidance threshold of the two hermit crab species to increasing water temperatures to help explain their intertidal distribution. We also compared the avoidance threshold of Cli. albidigitus to rising temperatures when presented alone and in the presence of chemical cues of its competitor to assess potential competitive niche exclusion. The avoidance threshold was measured in experimental tanks with a ramp that led from the water to an air-exposed platform; the threshold was defined as the temperature at which individuals emerged and remained air-exposed. Clibanarius albidigitus emerged at a higher temperature than its competitor, showing a higher thermal tolerance and potentially explaining its distribution in the upper intertidal. In the presence of Cal. californiensis, Cli. albidigitus emerged at lower temperature than when alone, likely as a strategy to reduce competition with stronger agonistic competitors, even at the cost of coping with harsh conditions. Our results support the hypothesis that competitive habitat exclusion contributes to explaining hermit crab assemblages.

Solving multispecies population games in continuous space and time

Game theory has emerged as an important tool to understand interacting populations in the last 50 years. Game theory has been applied to study population dynamics with optimal behavior in simple ecosystem models, but existing methods are generally not applicable to complex systems. In order to use game-theory for population dynamics in heterogeneous habitats, habitats are usually split into patches and game-theoretic methods are used to find optimal patch distributions at every instant. However, populations in the real world interact in continuous space, and the assumption of decisions based on perfect information is a large simplification. Here, we develop a method to study population dynamics for interacting populations, distributed optimally in continuous space. A continuous setting allows us to model bounded rationality, and its impact on population dynamics. This is made possible by our numerical advances in solving multiplayer games in continuous space. Our approach hinges on reformulating the instantaneous game, applying an advanced discretization method and modern optimization software to solve it. We apply the method to an idealized case involving the population dynamics and vertical distribution of forage fish preying on copepods. Incorporating continuous space and time, we can model the seasonal variation in the migration, separating the effects of light and population numbers. We arrive at qualitative agreement with empirical findings. Including bounded rationality gives rise to spatial distributions corresponding to reality, while the population dynamics for bounded rationality and complete rationality are equivalent. Our approach is general, and can easily be used for complex ecosystems.

Impact of disease on a two-patch eco-epidemic model in presence of prey dispersal

The present model is dealt with prey-predator interactions in two different patches where only prey species are allowed to disperse among the patches. Each of these two patches has different predator population but the predator in Patch-2 only is affected with a disease. The proposed model is biologically welldefined. Also, the feasibility of the equilibrium points and corresponding stability conditions are analysed. It is found that the disease among predator, even in one patch, makes an important role to control the whole system dynamics as it starts to oscillates by regulating the disease transmission rate. Moreover, the disease transmission rate has a stabilizing as well as destabilizing effect on the system dynamics. From the results, it is observed that a high dispersal rate decreases the count of infected predator in a patch in presence of prey dispersal. There is another interesting result: it is observed that the prey dispersal cannot destabilize the coexistence state, i.e., the system which is stable in absence of dispersal remains stable when the prey species disperse between two patches.

Plant coexistence mediated by adaptive foraging preferences of exploiters or mutualists

Coexistence of plants depends on their competition for common resources and indirect interactions mediated by shared exploiters or mutualists. These interactions are driven either by changes in animal abundance (density-mediated interactions, e.g., apparent competition), or by changes in animal preferences for plants (behaviorally-mediated interactions). This article studies effects of behaviorally-mediated interactions on two plant population dynamics and animal preference dynamics when animal densities are fixed. Animals can be either adaptive exploiters or adaptive mutualists (e.g., herbivores or pollinators) that maximize their fitness. Analysis of the model shows that adaptive animal preferences for plants can lead to multiple outcomes of plant coexistence with different levels of specialization or generalism for the mediator animal species. In particular, exploiter generalism promotes plant coexistence even when inter-specific competition is too strong to make plant coexistence possible without exploiters, and mutualist specialization promotes plant coexistence at alternative stable states when plant inter-specific competition is weak. Introducing a new concept of generalized isoclines allows us to fully analyze the model with respect to the strength of competitive interactions between plants (weak or strong), and the type of interaction between plants and animals (exploitation or mutualism).

Bacteria and game theory: the rise and fall of cooperation in spatially heterogeneous environments

One of the predictions of game theory is that cooperative behaviours are vulnerable to exploitation by selfish individuals, but this result seemingly contradicts the survival of cooperation observed in nature. In this review, we will introduce game theoretical concepts that lead to this conclusion and show how the spatial competition dynamics between microorganisms can be used to model the survival and maintenance of cooperation. In particular, we focus on how Escherichia coli bacteria with a growth advantage in stationary phase (GASP) phenotype maintain a proliferative phenotype when faced with overcrowding to gain a fitness advantage over wild-type populations. We review recent experimental approaches studying the growth dynamics of competing GASP and wild-type strains of E. coli inside interconnected microfabricated habitats and use a game theoretical approach to analyse the observed inter-species interactions. We describe how the use of evolutionary game theory and the ideal free distribution accurately models the spatial distribution of cooperative and selfish individuals in spatially heterogeneous environments. Using bacteria as a model system of cooperative and selfish behaviours may lead to a better understanding of the competition dynamics of other organisms-including tumour-host interactions during cancer development and metastasis.

Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

The population-dispersal dynamics for predator-prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator-prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.

Anomalous spatial redistribution of competing bacteria under starvation conditions

Bacterial cells evolved under prolonged stress often have a growth advantage in stationary phase (GASP); we expect GASP cells to maintain a proliferative state and dominate wild-type cells during starvation, especially when nutrients are limited and the medium has been conditioned. However, when we compete GASP mutants against wild-type cells in a chain of microfluidic microhabitat patches (MHPs) with alternating nutrient-rich and nutrient-limited regions, we observe the reverse effect: wild-type cells achieve maximum relative density under nutrient-limited conditions, while GASP cells dominate nutrient-rich regions. We explain this surprising observation in terms of ideal free distributions, where we show that wild-type cells maximize their fitness at high cell density by redistributing themselves to sparsely populated MHPs. At the microscopic level, we describe how biofilm formation also contributes to the population redistribution. We conclude by discussing the implications of these results for social interactions of more complex organisms.

Tactical population movements and distributions for ideally motivated competitors

The spatial distributions of populations are a reflection of underlying rules for movement behavior in the context of the environment encountered by individuals. Here I study how ideal directed movement--in which individuals travel in the direction offering the most immediate perceived improvement to their personal fitness--dictates the spatial position of two populations occupying the same relative niche and engaged in competition via interference to an individual's ability to gather resources. Drawing on the analytic derivation of equilibria, numerical simulations, and graphical assessments, I provide conditions under which sympatry, parapatry, or regional exclusion is expected during different phases of the community's development. I also demonstrate that specific competitive asymmetries produce distinguishable distributions and invasion patterns and identify which populations are found centrally or peripherally. Dynamic and dispersal equilibria were examined for differences in the sensitivity to spatial variations in fitness, per capita mortality, metabolic efficiency, the strength of interspecific interference, resource collection speed, and the optimal location of each population along an environmental cline. These asymmetries were studied both in isolation and pairwise in fitness trade-off scenarios.

Ratio- and predator-dependent functional forms for predators optimally foraging in patches

Functional forms of predator-prey interactions are developed for predators optimally foraging on prey distributed in patches. The model uses mean free-path-length theory to develop functional forms for two idealized behaviors of prey in patches. For congregating prey that maintain a fixed density, for example, fish schools, the predation rate has a ratio-dependent form, and predator interference depends only on predator density. For sessile prey, which maintain a fixed patch size, a new predator-dependent form emerges in which predator interference depends on both prey and predator densities. The Beddington-DeAngelis equation is a special case of the sessile form. The model provides behavioral and biological criteria with which to select the functional form and ranges of coefficients appropriate for a particular food web. Finally, the model illustrates that behavior is an essential factor in predator-prey dynamics.

Natural variation of male ornamental traits of the guppy, Poecilia reticulata

Male ornamental traits of the guppy, Poecilia reticulata, provide an outstanding example of natural variation in sex-linked male-advantageous traits that are shaped by both sexual and environmental selection. A substantial fraction of the underlying genes is known to be genetically linked to the sex-determining region on the differentiating Y-chromosome. Intercrosses between parental populations originating from geographically distant locations in East Trinidad and Cumaná (Venezuela) were used to study segregation of ornamental traits in male progeny. In addition, we performed backcrosses to compare segregation of ornaments in presence or absence of prominent traits linked to the Y-chromosome. Another backcross strategy involving XY females from the laboratory strain zebrinus maculatus allowed studying additive and dominant effects of alleles on two different Y-chromosomes on pattern formation. For genetic mapping, we have previously developed nuclear SNP markers linked to expressed genes, including several genes known to be important for pattern formation in other species. Of these candidate genes 15 were placed on 11 different linkage groups. Our phenotypic and genotypic analysis of progeny from mapping crosses and backcrosses suggests several genetic mechanisms that enhance natural variation, namely, additive effects of codominant alleles, suppressive actions of dominant alleles, and a complex interplay between sex-linked and autosomal cofactors.

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the "habitat selection game". Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species. For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker's matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called "two-species ESS". The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.

The role of behavioral dynamics in determining the patch distributions of interacting species

The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species-two-patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection.

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.

Predicting Resource Partitioning and Community Organization of Filter‐Feeding Dabbling Ducks from Functional Morphology

Resource partitioning due to interspecific differences in phenotype is a key component of ecological and evolutionary theory, but the relationship between morphology and resource use is poorly understood for most species. In addition, ecologists often assume that morphological differences cause distinct resource preferences between species. Using mechanistic models that combine bill morphology and kinetics, I show that filter-feeding dabbling ducks face a morphology-mediated trade-off between particle size selection and water filtration rate. When detritus is absent, mallards (Anas platyrhynchos) and northern shovelers (Anas clypeata) should maximize their intake rates and exhibit high overlap in prey size. When prey and detritus co-occur, species should separate prey from detritus by size, leading to reduced intake rates and size-based prey partitioning. Models for both species correctly predicted variation in water filtration rates, particle retention probabilities, and prey ingestion rates due to variation in prey size, the presence of detritus, and experimental modification of bill morphology. Because species have both shared and distinct resource preferences, duck communities should exhibit strong density-dependent niche shifts (i.e., centrifugal dynamics), a finding that contradicts previous studies that assumed that ducks have distinct resource preferences only. Centrifugal dynamics may be widespread among filter feeders because of the common cost of separating prey from detritus.

A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments

In this article we construct Lyapunov functions for models described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.

Macrophyte refuges, prey behaviour and trophic interactions: consequences for lake water clarity

Macrophytes may enhance grazing on phytoplankton by providing a refuge for zooplankton against fish predation. Loss of macrophytes can trigger sudden degradation of water clarity (regime shift) in lakes. However, the presence of piscivores may drive planktivorous fish to take refuge amongst littoral macrophytes. To address the possibility of regime shifts, I here constructed an empirically based model that combined population dynamics of organisms with game theory for optimal habitat selection, taking into consideration the trophic structure, lake size and eutrophication. The model showed that macrophytes generally acted as a refuge for zooplankton, rather than for fish. The model predicted that regime shifts were more likely in small, shallow lakes and that the presence of macrophytes raised the possibility of regime shifts. The present study demonstrated that the fast dynamics of animal behaviour could lead to regime shifts, in connection with slower variables such as nutrient loading.

A game-theoretic model for punctuated equilibrium: Species invasion and stasis through coevolution

A general theory of coevolution is developed that combines the ecological effects of species' densities with the evolutionary effects of changing phenotypes. Our approach also treats the evolutionary changes between coevolving species with discreet traits after the appearance of a new species. We apply this approach to habitat selection models where new species first emerge through competitive selection in an isolated habitat. This successful invasion is quickly followed by evolutionary changes in behavior when this species discovers the other habitat, leading to punctuated equilibrium as the final outcome.

Ecological Specialization of Mixotrophic Plankton in a Mixed Water Column

In recent years, the population dynamics of plankton in light- or nutrient-limited environments have been studied extensively. Their evolutionary dynamics, however, have received much less attention. Here, we used a modeling approach to study the evolutionary behavior of a population of plankton living in a mixed water column. Initially, the organisms are mixotrophic and thus have both autotrophic and heterotrophic abilities. Through evolution of their trophic preferences, however, they can specialize into separate autotrophs and heterotrophs. It was found that the light intensity gradient enables evolutionary branching and thus may result in the ecological specialization of the mixotrophs. By affecting the gradient, other environmental properties also acquire influence on this evolutionary process. Intermediate mixing intensities, large mixing depths, and high nutrient densities were found to facilitate evolutionary branching and thus specialization. Later results may explain why mixotrophs are often more dominant in oligotrophic systems while specialist strategies are associated with eutrophic systems.

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.

Ideal free distributions when resources undergo population dynamics

This study examines the influence of optimal patch choice by consumers on resource population dynamics and on consumer distribution in a two patch environment. The evolutionarily stable strategy which describes animal distributions across habitat patches is called the ideal free distribution (IFD) strategy. Two mechanisms that lead to the IFD are: (1) direct consumer competition such as interference, and (2) exploitative competition for resources. This article focuses on the second mechanism by assuming that resources undergo population dynamics while consumer abundance is fixed. Two models of resource growth are considered in detail: the exponential and the logistic. The corresponding consumer IFD is derived for each of these two models, assuming that consumers behave adaptively by moving to the patch which provides them with the highest fitness. This derivation does not require that resources are at an equilibrium, and it provides, for each resource density, the corresponding distribution of consumers. The article suggests that adaptive patch choice by consumers decreases between patch heterogeneity in resource levels and weakens the apparent competition between resources. The results for a single consumer population are extended for two competing consumer populations. The corresponding IFD is computed as a function of the two consumer densities. This allows for the analytical description of isolegs which are the boundary lines, in the two consumer density phase space, separating regions where qualitatively different habitat preferences are predicted.